Robustness of the rotor-router mechanism

Evangelos Bampas, Leszek Ga̧sieniec, Ralf Klasing, Adrian Kosowski, Tomasz Radzik

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

We consider the model of exploration of an undirected graph G by a single agent which is called the rotor-router mechanism or the Propp machine (among other names). Let πv indicate the edge adjacent to a node v which the agent took on its last exit from v. The next time when the agent enters node v, first a "rotor" at node v advances pointer πv to the edge which is next after the edge πv in a fixed cyclic order of the edges adjacent to v. Then the agent is directed onto edge πv to move to the next node. It was shown before that after initial O(mD) steps, the agent periodically follows one established Eulerian cycle, that is, in each period of 2m consecutive steps the agent traverses each edge exactly twice, once in each direction. The parameters m and D are the number of edges in G and the diameter of G. We investigate robustness of such exploration in presence of faults in the pointers πv or dynamic changes in the graph. We show that after the exploration establishes an Eulerian cycle, (i) if at some step the values of k pointers πv are arbitrarily changed, then a new Eulerian cycle is established within O(km) steps; (ii) if at some step k edges are added to the graph, then a new Eulerian cycle is established within O(km) steps; (iii) if at some step an edge is deleted from the graph, then a new Eulerian cycle is established within O(γm) steps, where γ is the smallest number of edges in a cycle in graph G containing the deleted edge. Our proofs are based on the relation between Eulerian cycles and spanning trees known as the "BEST" Theorem (after de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte).

Original languageEnglish (US)
Title of host publicationPrinciples of Distributed Systems - 13th International Conference, OPODIS 2009, Proceedings
Pages345-358
Number of pages14
DOIs
StatePublished - 2009
Event13th International Conference on Principles of Distributed Systems, OPODIS 2009 - Nimes, France
Duration: Dec 15 2009Dec 18 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5923 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Principles of Distributed Systems, OPODIS 2009
CountryFrance
CityNimes
Period12/15/0912/18/09

Keywords

  • Dynamic graphs
  • Graph exploration
  • Network faults
  • Propp machine
  • Rotor-router mechanism

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Bampas, E., Ga̧sieniec, L., Klasing, R., Kosowski, A., & Radzik, T. (2009). Robustness of the rotor-router mechanism. In Principles of Distributed Systems - 13th International Conference, OPODIS 2009, Proceedings (pp. 345-358). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5923 LNCS). https://doi.org/10.1007/978-3-642-10877-8_27